Question: Convert $1011001_2$ to base 4.
Answer: Since $2^2 = 4$, we can convert directly to base 4 by pairing digits together starting from the right side of our base 2 integer:  \begin{align*} 01_2 &= 1_4
\\ 01_2 &= 1_4
\\ 10_2 &= 2_4
\\ 01_2 &= 1_4
\end{align*}  Putting the base 4 digits together, we get $1011001_2 = \boxed{1121_4}$.